A105852 -id:A105852 - cp's OEIS frontend

A105827 a(n) = sigma(n) (mod 8).

1, 3, 4, 7, 6, 4, 0, 7, 5, 2, 4, 4, 6, 0, 0, 7, 2, 7, 4, 2, 0, 4, 0, 4, 7, 2, 0, 0, 6, 0, 0, 7, 0, 6, 0, 3, 6, 4, 0, 2, 2, 0, 4, 4, 6, 0, 0, 4, 1, 5, 0, 2, 6, 0, 0, 0, 0, 2, 4, 0, 6, 0, 0, 7, 4, 0, 4, 6, 0, 0, 0, 3, 2, 2, 4, 4, 0, 0, 0, 2, 1, 6, 4, 0, 4, 4, 0, 4, 2, 2, 0, 0, 0, 0, 0, 4, 2, 3, 4, 1, 6, 0, 0, 2, 0

Offset: 1

Shyam Sunder Gupta, May 05 2005

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to sums of divisors

Cf. A000203.

Sequences sigma(n) mod k: A053866 (k=2), A074941 (k=3), A105824 (k=4), A105825 (k=5), A084301 (k=6), A105826 (k=7), A105827 (k=8), A105852 (k=9), A105853 (k=10).

A105827:= (n-> numtheory[sigma](n) mod 8):
seq (A105827(n), n=1..105); # Jani Melik, Jan 26 2011

PARI
```
a(n)=sigma(n)%8
```

A105853 a(n) = sigma(n) (mod 10), i.e., unit's digit of sigma(n).

Original entry on oeis.org

1, 3, 4, 7, 6, 2, 8, 5, 3, 8, 2, 8, 4, 4, 4, 1, 8, 9, 0, 2, 2, 6, 4, 0, 1, 2, 0, 6, 0, 2, 2, 3, 8, 4, 8, 1, 8, 0, 6, 0, 2, 6, 4, 4, 8, 2, 8, 4, 7, 3, 2, 8, 4, 0, 2, 0, 0, 0, 0, 8, 2, 6, 4, 7, 4, 4, 8, 6, 6, 4, 2, 5, 4, 4, 4, 0, 6, 8, 0, 6, 1, 6, 4, 4, 8, 2, 0, 0, 0, 4, 2, 8, 8, 4, 0, 2, 8, 1, 6, 7, 2, 6, 4, 0, 2

Offset: 1

Shyam Sunder Gupta, May 05 2005

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000203, A010879.

Sequences sigma(n) mod k: A053866 (k=2), A074941 (k=3), A105824 (k=4), A105825 (k=5), A084301 (k=6), A105826 (k=7), A105827 (k=8), A105852 (k=9), A105853 (k=10).

A105853:=n->(numtheory)[sigma](n) mod 10: seq(A105853(n), n=1..180); # Wesley Ivan Hurt, Nov 07 2017

Mod[DivisorSigma[1,Range[110]],10] (* Harvey P. Dale, May 20 2019 *)

PARI
```
a(n)=sigma(n)%10
```

a(n) = A010879(A000203(n)). - Michel Marcus, Jul 26 2017

A240597 Numbers k such that sigma(k) == k (mod 9).

Original entry on oeis.org

1, 15, 24, 42, 60, 64, 69, 78, 90, 100, 114, 123, 133, 147, 153, 177, 186, 198, 222, 231, 240, 258, 259, 270, 276, 288, 289, 306, 339, 360, 366, 393, 402, 403, 414, 429, 438, 447, 459, 474, 477, 492, 495, 501, 507, 511, 522, 582, 588, 594, 600

Offset: 1

Ivan N. Ianakiev, Sep 13 2014

That is, numbers k that satisfy the following:
A010878(k) = A105852(k) or A010878(k) = A010878(A000203(k)).
A010888(k) = A190998(k) or A010888(k) = A010888(A000203(k)).

			sigma(15) = 24. 24 == 15 (mod 9), therefore 15 is in the sequence.

Ivan N. Ianakiev, Table of n, a(n) for n = 1..10000

Cf. A000203, A190998, A010878, A105852, A010888.

Select[Range[1000],Mod[#,9]==Mod[DivisorSigma[1,#],9]&]

A010888(a(n)) = A010888(A000203(a(n))).

A010888(a(n)) = A190998(a(n)).

cp's OEIS Frontend

A105827 a(n) = sigma(n) (mod 8).

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A105853 a(n) = sigma(n) (mod 10), i.e., unit's digit of sigma(n).

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Maple

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A240597 Numbers k such that sigma(k) == k (mod 9).

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